Abstract
Mathematical modeling with the help of numerical coding of graphs has been used in the different fields of science, especially in chemistry for the studies of the molecular structures. It also plays a vital role in the study of the quantitative structure activities relationship (QSAR) and quantitative structure properties relationship (QSPR) models. Todeshine et al. (2010) and Eliasi et al. (2012) defined two different versions of the 1st multiplicative Zagreb index as ∏Γ=∏p∈VΓdΓp2 and ∏1Γ=∏pq∈EΓdΓp+dΓq, respectively. In the same paper of Todeshine, they also defined the 2nd multiplicative Zagreb index as ∏2Γ=∏pq∈EΓdΓp×dΓq. Recently, Liu et al. [IEEE Access; 7(2019); 105479–-105488] defined the generalized subdivision-related operations of graphs and obtained the generalized F-sum graphs using these operations. They also computed the first and second Zagreb indices of the newly defined generalized F-sum graphs. In this paper, we extend this study and compute the upper bonds of the first multiplicative Zagreb and second multiplicative Zagreb indices of the generalized F-sum graphs. At the end, some particular results as applications of the obtained results for alkane are also included.
Highlights
We extend this study and compute the upper bonds of the first multiplicative Zagreb and second multiplicative Zagreb indices of the generalized F-sum graphs
Introduction e numerical demonstration of a molecular graph can be assumed as a single number, commonly known as topological index (TI). ere are many interesting and significant results about TIs to study the different properties of chemical compounds such as chromatographic retention times, heat of formation and evaporation, flash point, viscosity, freezing, boiling and melting point, octanol-water partition coefficient, surface tension, stability, temperature, density, weight, polarizability, connectivity, and solubility
Different impressive TIs are introduced in molecular graph theory [20,21], but the degree-based TIs are famous than others, see [22]
Summary
Ey computed the first and second Zagreb indices of the newly defined generalized F-sum graphs. We extend this study and compute the upper bonds of the first multiplicative Zagreb and second multiplicative Zagreb indices of the generalized F-sum graphs. [28], and Liu et al [29] determined the 1st and 2nd Zagreb Journal of Chemistry indices, F-index, Hyper-Zagreb index, and the 1st general Zagreb index of F1-sum graphs.
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